As I discuss in this question, by far the most popular school of Hindu philosophy is the Vedanta school. But there are five other Astika or orthodox schools of Hindu philosophy: Purva Mimamsa, Samkhya, Yoga, Vaisheshika, and Nyaya. My question is about the Samkhya school, founded by the sage Kapila. There are three works which are variously claimed to be the oldest surviving work of the Samkhya school: Kapila's Samkhya Sutras, Kapila's Tattva Samasa, and Ishwara Krishna's Samkhya Karika. Of these three, scholars consider the Samkhya Karika to be the oldest; the original defining work of the Samkhya school was composed by Kapila, but scholars believe that work is lost and that the Samkhya Sutras and Tattva Samasa are just later works attributed to Kapila.

But my question is, what is the Guru Parampara of Ishwara Krishna, the author of the Samkhya Karika? How many generations removed is he from Kapila?

This sacred and supreme (Knowledge), the sage (Kapila) gave to Āsuri out of compassion. Āsuri (gave it) to Pañcaśikha, who elaborated the doctrine. Handed down by tradition of disciples, this was summarised in Ārya verses by Iśvarakṛṣṇa of noble mind, having fully understood the demonstrated truth.
The topics of these seventy verses are those of the entire Ṣaṣṭitantra; they are devoid of anecdotes and also omit discussions of rival views.

So Kapila's shishya was Asuri, whose shishya was Panchashikha. But what is the Guru Parampara between Panchashikha and Ishwara Krishna? Do any commentaries on the Samkhya Karika shed light on this?

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Most of the commentaries on the Samkhya Karika, including Gaudapada's Samkhya Karika Bhashya (which you can read here), Vachaspati Mishra's Samkhya Tattva Kaumudi (which you can read here), and Narayana Tirtha's Samkhya Chandrika (which you can read here), don't contain any information on Ishwara Krishna's Guru Parampara. But I found two commentaries that provide some information:

The Yuktidipika, which is an ancient commentary of unknown authorship discovered in the 1930's. Here is what this excerpt from the Yukti Dipika says:

In brief this shastra is (handed over to us) through [gap in the manuscript] Harita, Vaddhali, Kairat, Paurika, Arshbheshvara, Panchadhikarana, Patanjali, Varsaganya, Kaundinya, Muka, etc.

But it's unclear whether this is the Guru Parampara of Ishwara Krishna or just the Guru Parampara of the author of the Yuktidipika. In any case, it's interesting that the Patanjali would be mentioned, considering that he's the Sutrakara of the Yoga school.

The Suvarna Saptati, another ancient commentary of unknown authorship which is lost in the original Sanskrit, but exists in a Chinese translation written by the 6th century Buddhist philosopher Paramartha. Here what this excerpt from Paramartha's Chinese version says:

That knowledge came from Kapila to Asuri, who transmitted it to Panchashikha; Panchashikha gave it to Ho-kia, Ho-kia to Uluka, Uluka to Po-po'-li, Po-po'-li to Ishvarakrishna. By that transmission Ishvarakrishna obtained the knowledge.

Some of the names are unclear because they're Chinese equivalents of Sanskrit names, but the translator speculates that Ho-Kia refers to Gargya and Po-po'-li refers to Vrisa, which may be a short form for Varsaganya who is referenced in the Yuktidipika quote. In any case, it's interesting that Uluka is mentioned, because that's another name for Kanada, the founder of the Vaisheshika school.